[General Questions and Answers] pyroboy1080:
Okay, from the best of my understanding, here we go:

1: Rooting. To understand this, we must consider a computer, running linux, windows, or mac. In windows, the "Administrator" account is similar to the root account in linux and mac. Basically if you have root privileges in a system, you can modify every part of the filesystem, as well as perform any tasks the system is equipped to handle. Basically achieving root on an android device means that you can unlock the ability to flash roms, mod, and otherwise hack your device any which way you like. Nearly every model of android device has been rooted, so in most cases, yes you can root XXXXX phone. Also, since you're just gaining privileges, you can root without losing any data, apps, or settings.

2: Recovery. This is a long standing concept in SoC/Embedded device hacking. Basically it is a minimal operating system that performs some very basic, but very important tasks. The reason for it is so that you can write to the necessary areas on the NAND, which would be "busy" while android is booted. This offers a way to access the necessary partitions and write data to them while the data is not being accessed. It's also useful for backing up your NAND. Hence the name "nandroid."

3: ROM. By definition, it means "Read Only Memory." This is a chip on the board. ROM has evolved over the years. It started out as a chip that was sensitive to UV light. The earliest ROMs were "flashed" to a device by stenciling out the pathways and exposing the chip to UV radiation. Nowadays, we have fancy EEPROMs instead, which stands for Electronically Erasable Programmable Read Only Memory. This means that you can "flash" the chip by means of software, namely via Recovery mode in our case. Different ROMs have different features. They are all variations on source code made available by AOSP, or the android open source project. Some projects have their own code tracking, such as CyanogenMod. In most devices, you must be rooted to be able to install a ROM, however it is not explicitly necessary. A bit vague, I suppose. Specifically the tablet I own, the WITS a81e, you can flash a ROM to it just by putting the correct files on the TF card. This is not very common with phones, however. Flashing any rom that is not just a newer version of your current ROM will require a full format. For instance, if you have cyanogenmod and switch to a Sense or Blur ROM, you must format, but if you update from CM6 to CM6.1 you will not need to wipe. How can you trust ROM's? Well the best way to know is to either roll your own, or go with CyanogenMod, as their source is freely and easily available for scrutiny and improvement, along with a nice changelog tracker.

4. Kernels. A kernel is basically the most low level part of an operating system. It interfaces directly with the processor and provides all instruction for operation. Linux is technically not an operating system, it's a Kernel. The different distributions have the Linux kernel, and use their own different User Interfaces. Different kernels in android devices can allow you to overclock. There are many choices in kernels, and the features they offer. Some features are BFS/CFS which is the priority scheduling of processes. Some kernels allow you to charge your battery differently and conserve life. These are often called battery kernels. Also, some kernels unlock extra multitouch points in certain devices. There are different versions of the linux kernel, with many improvements with each iteration. Currently, the latest kernel available that I know of for android devices is 2.6.37. The froyo default kernel was a 2.6.32. I wish I knew a bit more about kernels, however this is about all I know. Perhaps someone could help us out and expand on this a bit?